Margin of Error Calculator

What is Margin of Error?

Margin of error is a statistical measurement that allows researchers to gauge how accurate survey results are. The figure shows how much the results from a random sample survey can differ from the actual population.

The larger the margin of error, the less confidence one should have in the results of a survey.

The margin of error is usually shown as a plus or minus percentage. This helps us figure out a range of possible percentages when we compare survey results to real-world data.

For example, if a survey says 48% of people prefer Product A over Product B, with a margin of error of +/- 5%, the actual range might be anywhere from 43% to 53%.

How to Calculate Margin of Error [With Formula]

n = sample size • σ = population standard deviation • z = z-score

1. Figure out your sample size: This is the number of people you surveyed or measured in your study.
   
   
2. Determine the confidence level: This is usually set at 95%, which means if you did the same survey many times, you'd expect the results to be within the margin of error 95 times out of 100.
   
   
3. Find the standard deviation: This measures how much your data varies from the average. If you don't know this, you can use 0.5 for yes/no questions or 0.25 for questions with multiple choices.
   
   
4. Plug everything into the formula: The formula for margin of error is: Margin of Error = (Z-score) * (Standard Deviation / √Sample Size)
   
   The Z-score is a number you can find in a table based on your confidence level. For a 95% confidence level, the Z-score is usually around 1.96.
   
   
5. Calculate it: Once you have your Z-score, standard deviation, and sample size, just plug them into the formula, and you'll get your margin of error!

And that's it! You've calculated the margin of error. It tells you how much your survey results might vary from the actual population.

Margin of Error Example

Let's walk through an example of calculating the margin of error using the formula.

Let's say we conducted a survey asking 500 people whether they prefer coffee or tea. We want to calculate the margin of error for this survey with a 95% confidence level.

1. Sample size (n): 500
2. Confidence level (C.L.): 95% (Z-score for 95% confidence level is approximately 1.96)
3. Standard deviation (σ): Since this is a yes/no question (coffee or tea), we can use a standard deviation of 0.5.

Now, let's plug these values into the formula:

Margin of Error = (Z-score) * (Standard Deviation / √Sample Size)

Margin of Error = (1.96) * (0.5 / √500)

To simplify, √500 is approximately 22.36:

Margin of Error ≈ (1.96) * (0.5 / 22.36)

Now, calculate:

Margin of Error ≈ (1.96) * (0.0224)

Margin of Error ≈ 0.043904

So, the margin of error for our survey is approximately 0.043904, or about 4.39%.

This means that if we were to conduct the same survey many times, we could expect the results to be within plus or minus 4.39% of the actual population preferences 95% of the time.

Confidence Interval vs. Confidence Level

The confidence interval and confidence level are closely related concepts in market research.

The confidence level represents the probability that the calculated confidence interval contains the true population parameter.

For example, a 95% confidence level means that if we were to take many samples and construct a confidence interval from each sample, approximately 95% of those intervals would contain the true population parameter.

On the other hand, the confidence interval is the range of values within which we estimate the true population parameter to lie.

It is expressed as an interval around the sample statistic, such as the mean or proportion, and reflects the precision of our estimate.

In short, the confidence level tells us how sure we are that the interval captures the true value, while the confidence interval gives us the range of values we believe the true value falls within.

How Many Survey Completes Do I Need?

As a starting point, we typically consider 400 completes to be a balance between the costs of surveying individuals and reliability of results.

With this number of completes, the margin of error is just below our best-practice and industry standard of +/-5% margin of error, providing you with representative survey results of the population.

The number of survey completes needed is ultimately reliant on how you plan to use the data.

For example, if you plan to focus on subsets of respondents (i.e. 25 to 34-year-olds) during analysis or you plan to make the findings available for public consumption, minimizing margin of error will be important.

The chart below illustrates this point. 

Margin of Error by Survey Sample Size

Note, the margin of error in this chart assumes a large population size. The margin of error calculator above can be used to determine how many survey completes you will need to obtain a +/-5% margin of error with a smaller population.